I was watching a show the other day and a guy was building just a wire mesh faraday cage. He said it would protect his electronic equipment in the event of a massive solar flare or EMP from a nuclear weapon.

It also rather depends on what you are trying to protect and from what. A solar flare of a level posing a minor risk is one thing, a deliberately engineered military EMP may be much worse, though just how much is presumably classified information.

I don't have a clue about the energies involved, but might a large thin wire mesh cage simply melt due to the currents involved? Would this happen outside the radius survivable by humans, with the possible exception of users of pacemakers or other electrical or conductive prostheses? Grim ideas.

I have also worked in screen rooms, but they were trying to not let any radiation out from the secret transmitters I was working on. I was amazed! Hundreds of watts at hundreds of megahurts, with the carrier cranked all the way to square waves, into a "cantenna" and it was still a secret, 20 feet away.

Now we have somebody tying to stop a walkie talkie and it doesn't work? Got me stumped!

On the other thread, the OP is only trying to stop the walkie-talkie by the attenuation of a screening cage. No jamming or disruptive extra transmitter is involved, but since the transmitter and receiver are only metres apart, much closer than their ultimate range, a very large attenuation will be needed.